Abstract: In recent years, kernel density estimation has been exploited by computerscientists to model machine learning problems. The kernel density estimationbased approaches are of interest due to the low time complexity of either Onor On*logn for constructing a classifier, where n is the number of samplinginstances. Concerning design of kernel density estimators, one essential issueis how fast the pointwise mean square error MSE and-or the integrated meansquare error IMSE diminish as the number of sampling instances increases. Inthis article, it is shown that with the proposed kernel function it is feasibleto make the pointwise MSE of the density estimator converge at On^-2-3regardless of the dimension of the vector space, provided that the probabilitydensity function at the point of interest meets certain conditions.